Lower and Upper Solutions for General Two-Point Fractional Order Boundary Value Problems

Lower and Upper Solutions for General Two-Point Fractional Order Boundary Value Problems

K. R. Prasad, B. M. B. Krushna

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Abstract

This paper establishes the existence of a positive solution of fractional order two-point boundary value problem, ay(t)+ f(t, y(t)) = 0,t ∈ [a, b], y(a)=0,y ′ (a)=0, CDq2 y(b) − (Dq3 y(a)=0, Dq1+ a+ a+ where Daqi + ,i =1, 2, 3 are the standard Riemann-Liouville fractional order derivatives, 2 a ≥ 0, by an application of lower and upper solution method and fixed-point theorems.

 

Keywords

Fractional derivative, Boundary value problem, Two-point, Green’s function, Positive solution.